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At the heart of a contentious court case between a company and its ex-parent is an accounting question that has been dogging corporate finance executives for the better part of a year. That is, what is the fair value of a company’s contingent liabilities? The answer may help a bankruptcy court determine whether chemical maker Tronox Inc. was solvent at the time of its initial public offering in November 2005.

If it turns out Tronox was insolvent, it could lend credence to its claims against the former parent, Kerr-McGee, now part of Anadarko Petroleum, which Tronox also is suing. However, coming up with a contingent liability valuation won’t be easy. The challenge is in putting a price tag on future losses, a notion that is already steeped in controversy.

Tronox claims that Kerr-McGee orchestrated a scheme to sell itself to Anadarko after it “dumped” contingent liabilities on Tronox. The chemical company also alleges that Kerr-McGee misrepresented Tronox’s financial health at the time of its IPO, and set up the chemical company to fail by leaving it “undercapitalized” and laden with environmental contingent liabilities. By January 2009, Tronox had filed for Chapter 11.

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In response to the lawsuit, Anadarko filed a motion in bankruptcy court to dismiss the case, contending that Tronox’s allegations were an “attempt to rewrite history” and unjustifiably blame its poor financial condition on Kerr-McGee. Anadarko, in its motion, said the Tronox claims were “not only misleading, but insufficient as a matter of law.”

For example, Anadarko contends Tronox did not show signs of insolvency until three years after the IPO. Before that, it generated $16.6 million more net income in the first quarter of 2006 than it did for the same period in 2005, made optional prepayments on term loans, and did not draw down on its $250 million credit facility until early 2008. Tronox “is not very unique” in that the bankruptcy courts are filled with companies, including other chemical makers, that are in financial straits because of the economy, Anadarko spokesman John Christiansen told CFO.com.

From a financial-statement perspective, Tronox was solvent at the time of the IPO. As reported under generally accepted accounting principles, Tronox recorded $1.76 billion in total assets and $1.27 billion in total liabilities, leaving $490 million in equity on its balance sheet. Its reserve for environmental contingent liabilities, which is an off-balance-sheet entry, was $224 million at the time of the IPO.

But accounting entries don’t count for much in bankruptcy proceedings, experts say. “GAAP isn’t relevant” in bankruptcy court, contends Jeffery Manning, a managing director of Trenwith Securities and a frequent expert witness on the subject of valuations. He explains that bankruptcy judges are looking not for the “rear-view mirror” perspective that GAAP provides, but rather for a market or fair-value assessment of assets and liabilities to determine the eventual distribution among creditors.

As a result, a bankruptcy court typically would bring back on to the balance sheet all of the off-balance-sheet assets and liabilities, including environmental contingent liabilities. According to one recent study of such liabilities of oil and chemical companies, the estimated fair value of Tronox’s liabilities easily outstripped the fair value of its assets at the time of the IPO in November 2005. According to the study, then, the company was actually bankrupt when it went public.

In the study, parts of which are featured in this month’s issue of CFO magazine, Greg Rogers, president of consultancy Advanced Environmental Dimensions, estimates that the fair value of Tronox’s environmental contingent liabilities was $1.2 billion — far beyond the $224 million reserve the company reported — on the date it went public. That is more than twice the company’s equity of $556 million, as valued by investors in the IPO.

Rogers used a proprietary set of financial analytics and what he characterizes as a conservative 6.5 multiple applied to the $224 million reported reserve to calculate the fair value of the company’s liabilities. His study, which is based on public financial data for 24 oil, gas, and chemical companies, illustrates that despite spending millions each year on environmental cleanup, most of the companies take charges every year to replenish their environmental reserves.

If the study’s calculation for Tronox is a reasonable estimate of fair value, that would put its contingent environmental liabilities for 2005 at just over $1.4 billion, while total liabilities would add up to about $2.69 billion, far above its total book assets ($1.27 billion), and probably much higher than any reasonable fair-value estimate of the company’s assets.

To assure that an apples-to-apples comparison is being made, the bankruptcy judges would have to look at not only the fair value of Tronox’s liabilities but also the fair value (rather than the book value) of its assets. One quick way to scratch out a fair-value asset calculation is to look at the IPO proceeds, considered by most valuation experts as an observable market price.

In the IPO, investors valued the company’s total equity at $566 million, about 15% higher than its reported equity of $490 million. So assuming investors accepted the $1.27 billion book value of the company’s liabilities as a reasonable proxy for their fair value, they considered the fair value of the total assets to be at least $1.76 billion, or at most 15% more than that — meaning that Tronox was carrying more liabilities than assets.

Still, agreeing on which fair-value calculation to use is a complicated matter. And trying to figure out which models and methods a bankruptcy judge will deem useful is even tougher. For instance, John LaLiberte, a partner with the law firm Sherin & Lodgen, says bankruptcy judges will also consider “a probability analysis” related to contingent liabilities to figure out what percentage of the estimated losses the company will likely book in the future.

Complicating matters further is the fact that the concept of fair value has been vilified over the past year by bankers and their lobbyists who hate the idea that accounting rule-makers were requiring mark-to-market measures of financial liabilities during a credit crisis. On the other hand, critics with more conservative views said fair-value accounting didn’t go far enough to rein in abuse because it was open to a significant amount of management discretion. To be sure, the accounting rule known as FAS 5 allows a healthy dose of discretion with regard to booking contingent liabilities.

The controversy surrounding the fair-value calculation is just one more stumbling block in an already complicated family feud that the judges will have to sort out without the help of accounting rules. “GAAP is a method to keep score, but it doesn’t necessarily have anything to do with valuation,” says Manning.